Multi-step Prediction of Sintering Terminal Point Based on PBT-DeepTCN and Digital Twin

doi:10.12068/j.issn.1005-3026.2026.20240126

Abstract

Abstract:

The position of the sintering terminal point is a key parameter that affects the quality and production efficiency of sinter. To improve insufficient guidance， poor timeliness， and weak visualization effect in sintering terminal point prediction， a five-dimensional digital twin model was constructed， including physical entity， virtual environment， multi-step prediction， twin data， and virtual and real connection， which provided process parameter monitoring and optimization guidance for the sintering process. In terms of prediction， the data was first preprocessed， and then the feature variables were screened by grey relation analysis （GRA）. Finally， the deep temporal convolutional network （DeepTCN）by using population based training（PBT） was constructed for multi-step prediction of the sintering terminal point. The experimental results show that the proposed digital twin model has high prediction accuracy under different prediction steps， and it provides advanced ideas and technical methods for digital and intelligent transformation in the sintering field.

Key words: sintering terminal point, multi-step prediction, digital twin, deep temporal convolutional network, hyperparameter optimization

CLC Number:

TF 046

Xiao-long SONG, Xiao-tong LI, Huan YANG, Zhao-xia WU. Multi-step Prediction of Sintering Terminal Point Based on PBT-DeepTCN and Digital Twin[J]. Journal of Northeastern University(Natural Science), 2026, 47(1): 99-106.

Figures/Tables 10

Fig.1 Flow chart of sintering process

Fig.2 Digital twin system framework

Table 1 Grey relational degree ranking of feature

序号	变量名称	灰色关联度
1	20#风箱废气温度/ºC	0.277 1
2	焦粉下料量/( $t ⋅ h - 1$ )	0.274 2
3	7#风箱负压/kPa	0.267 4
4	7#风箱废气温度/ºC	0.243 4
5	1#风箱废气温度/ºC	0.230 6
6	w(混料氧化钙)/%	0.222 1
7	3#风箱废气温度/ºC	0.190 8
8	11#风箱负压/kPa	0.189 1
9	13#风箱废气温度/ºC	0.186 1
10	w（混料水分）/%	0.176 1
11	2#风箱废气温度/ºC	0.172 3
12	1#风箱负压/kPa	0.164 2
13	w(混料二氧化硅)/%	0.161 7
14	烧结机机速/( $m ⋅ m i n - 1$ )	0.161 3
15	2#风箱负压/kPa	0.159 7

Table 1 Grey relational degree ranking of feature

序号	变量名称	灰色关联度
1	20#风箱废气温度/ºC	0.277 1
2	焦粉下料量/( $t ⋅ h - 1$ )	0.274 2
3	7#风箱负压/kPa	0.267 4
4	7#风箱废气温度/ºC	0.243 4
5	1#风箱废气温度/ºC	0.230 6
6	w(混料氧化钙)/%	0.222 1
7	3#风箱废气温度/ºC	0.190 8
8	11#风箱负压/kPa	0.189 1
9	13#风箱废气温度/ºC	0.186 1
10	w（混料水分）/%	0.176 1
11	2#风箱废气温度/ºC	0.172 3
12	1#风箱负压/kPa	0.164 2
13	w(混料二氧化硅)/%	0.161 7
14	烧结机机速/( $m ⋅ m i n - 1$ )	0.161 3
15	2#风箱负压/kPa	0.159 7

Fig.3 Multi-step prediction process

Fig.4 Structure of DeepTCN

Fig.5 Encoder and decoder modules

Table 2 Adjustment range of hyperparameters

超参数名称	寻优范围
学习率	[0.000 1 0.01]
批处理大小	[4 32]
卷积核大小	[25]
滤波器数量	[110]
输入序列长度	[10 50]

Fig.6 Prediction results of sintering terminal point

Table 3 Comparison results of different models

预测步长	对比模型	$e R M S$	$e M A$	R²
t+1	CNN	0.035 1	0.028 0	0.410 2
	LSTM	0.022 8	0.018 8	0.752 6
	DeepTCN	0.013 4	0.011 3	0.913 8
	PBT- DeepTCN	0.010 4	0.008 0	0.948 3
t+4	CNN	0.038 6	0.027 7	0.288 0
	LSTM	0.029 3	0.023 8	0.590 6
	DeepTCN	0.014 0	0.010 3	0.824 5
	PBT-DeepTCN	0.018 8	0.016 3	0.882 6
t+8	CNN	0.042 9	0.031 0	0.120 2
	LSTM	0.032 9	0.027 3	0.484 4
	DeepTCN	0.023 8	0.020 3	0.725 2
	PBT-DeepTCN	0.021 0	0.017 8	0.769 1

Table 3 Comparison results of different models

预测步长	对比模型	$e R M S$	$e M A$	R²
t+1	CNN	0.035 1	0.028 0	0.410 2
	LSTM	0.022 8	0.018 8	0.752 6
	DeepTCN	0.013 4	0.011 3	0.913 8
	PBT- DeepTCN	0.010 4	0.008 0	0.948 3
t+4	CNN	0.038 6	0.027 7	0.288 0
	LSTM	0.029 3	0.023 8	0.590 6
	DeepTCN	0.014 0	0.010 3	0.824 5
	PBT-DeepTCN	0.018 8	0.016 3	0.882 6
t+8	CNN	0.042 9	0.031 0	0.120 2
	LSTM	0.032 9	0.027 3	0.484 4
	DeepTCN	0.023 8	0.020 3	0.725 2
	PBT-DeepTCN	0.021 0	0.017 8	0.769 1

Fig.7 Digital twin visual interface

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